Haven't run the game in a year or so and I decided to re-analyse the game for time saves and discovered that if I skipped the cross-country level by using the "give up" option in the paus menu that I can save way more time than intentionally failing the dressage levels by leaving the ring. So now each round I "give up" on the cross country and try to do the "dressage" levels as quickly as I can by balancing "errors in gait" with speed.

Still some optimisation in this with some small mistakes, but I'm pretty happy with it after a handful of attempts at the new strat.